Ising model for distribution networks

H. Hooyberghs* (Corresponding Author), S. Van Lombeek, C. Giuraniuc, B. Van Schaeybroeck, J. O. Indekeu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


An elementary Ising spin model is proposed for demonstrating cascading failures (breakdowns, blackouts, collapses, avalanches, etc.) that can occur in realistic networks for distribution and delivery by suppliers to consumers. A ferromagnetic Hamiltonian with quenched random fields results from policies that maximize the gap between demand and delivery. Such policies can arise in a competitive market where firms artificially create new demand, or in a solidarity environment where too high a demand cannot reasonably be met. Network failure in the context of a policy of solidarity is possible when an initially active state becomes metastable and decays to a stable inactive state. We explore the characteristics of the demand and delivery, as well as the topological properties, which make the distribution network susceptible of failure. An effective temperature is defined, which governs the strength of the activity fluctuations which can induce a collapse. Numerical results, obtained by Monte Carlo simulations of the model on (mainly) scale-free networks, are supplemented with analytic mean-field approximations to the geometrical random field fluctuations and the thermal spin fluctuations. The role of hubs versus poorly connected nodes in initiating the breakdown of network activity is illustrated and related to model parameters.

Original languageEnglish
Pages (from-to)168-191
Number of pages24
Journalphilosophical magazine
Issue number1-3
Early online date31 Oct 2011
Publication statusPublished - 1 Jan 2012

Bibliographical note

We thank economist Marc Lambrecht of K.U. Leuven for his interest in and his comments on this model. HH and BVS thank the FWO-Vlaanderen for support.


  • avalanche
  • blackout
  • breakdown
  • cascade
  • collapse
  • complex scale-free distribution network
  • failure
  • Ising model
  • random fields


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